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2 years ago

HELP ASAP ITS DUE RIGHT NOW

Mathematics

1 answer:

kirza4 [7]2 years ago

5 0

Answer:

440

Step-by-step explanation:

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Evaluate the interval (Calculus 2)

Darya [45]

Answer:

$2 \tan (6x)+2 \sec (6x)+\text{C}$

Step-by-step explanation:

Fundamental Theorem of Calculus

$\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))$

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given indefinite integral:

$\displaystyle \int \dfrac{12}{1-\sin (6x)}\:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Terms multiplied by constants}\\\\$\displaystyle \int a\:\text{f}(x)\:\text{d}x=a \int \text{f}(x) \:\text{d}x$\end{minipage}}$

If the terms are multiplied by constants, take them outside the integral:

$\implies 12\displaystyle \int \dfrac{1}{1-\sin (6x)}\:\:\text{d}x$

Multiply by the conjugate of 1 - sin(6x) :

$\implies 12\displaystyle \int \dfrac{1}{1-\sin (6x)} \cdot \dfrac{1+\sin(6x)}{1+\sin(6x)}\:\:\text{d}x$

$\implies 12\displaystyle \int \dfrac{1+\sin(6x)}{1-\sin^2(6x)} \:\:\text{d}x$

$\textsf{Use the identity} \quad \sin^2 x+ \cos^2 x=1:$

$\implies \sin^2 (6x) + \cos^2 (6x)=1$

$\implies \cos^2 (6x)=1- \sin^2 (6x)$

$\implies 12\displaystyle \int \dfrac{1+\sin(6x)}{\cos^2(6x)} \:\:\text{d}x$

Expand:

$\implies 12\displaystyle \int \dfrac{1}{\cos^2(6x)}+\dfrac{\sin(6x)}{\cos^2(6x)} \:\:\text{d}x$

$\textsf{Use the identities }\:\: \sec \theta=\dfrac{1}{\cos \theta} \textsf{ and } \tan\theta=\dfrac{\sin \theta}{\cos \theta}:$

$\implies 12\displaystyle \int \sec^2(6x)+\dfrac{\tan(6x)}{\cos(6x)} \:\:\text{d}x$

$\implies 12\displaystyle \int \sec^2(6x)+\tan(6x)\sec(6x) \:\:\text{d}x$

$\boxed{\begin{minipage}{5 cm}\underline{Integrating $\sec^2 kx$}\\\\$\displaystyle \int \sec^2 kx\:\text{d}x=\dfrac{1}{k} \tan kx\:\:(+\text{C})$\end{minipage}}$

$\boxed{\begin{minipage}{6 cm}\underline{Integrating $ \sec kx \tan kx$}\\\\$\displaystyle \int \sec kx \tan kx\:\text{d}x= \dfrac{1}{k}\sec kx\:\:(+\text{C})$\end{minipage}}$

$\implies 12 \left[\dfrac{1}{6} \tan (6x)+\dfrac{1}{6} \sec (6x) \right]+\text{C}$

Simplify:

$\implies \dfrac{12}{6} \tan (6x)+\dfrac{12}{6} \sec (6x)+\text{C}$

$\implies 2 \tan (6x)+2 \sec (6x)+\text{C}$

Learn more about indefinite integration here:

brainly.com/question/27805589

brainly.com/question/28155016

3 0

2 years ago

A rug is 12 feet wide and 15 1/2 feet long. What is the area of the rug?

fgiga [73]

Answer:

372 feet^2

Step-by-step explanation:

A=LW

A=(15 1/2)(12)=(31/2)(12)=(31/2)(24/2)=744/2=372

3 0

3 years ago

What is the inverse of 2/3?

jolli1 [7]

The inverse of 2/3
is 3/2.

Good Luck! :)

3 0

3 years ago

Read 2 more answers

Please help me

kifflom [539]

Answer:

Angle BCA is 74 degrees, angle MBC is 21, angle MCB is 37, and BMC is 122

Step-by-step explanation:

First off, MBC was an angle that was bisected by point M, meaning that if you took half of angle ABC, you would get your answer.

(0.5)(42)=21

Since you already have two angle measures, being ABC and BAC, you can find angle BCA by adding the two angle measures up, then subtracting by 180 to get your answer:

180=64+42+BCA, which your answer will be 74 degrees.

Now that you have found angle BCA, you take half of that angle measure to then find angle MCB, because point M bisected angles ABC, BAC, and BCA.

(0.5)(74)=37

Finally, since you have found the angles MBC and MCB, in order to find angle BMC you will have to do the same application for BCA:

180=21+37+BMC, which your answer will be 122 degrees.

Hope this helps!

7 0

3 years ago

If 9 : x = x:4, then x = _____. 36 18 24 6

borishaifa [10]

Solution: 9:x = x:4

⇛9/x = x/4

By doing cross multiplication, we get

⇛9(4) = x(x)

⇛36 = x²

⇛x² = 36

⇛x = √(36)

⇛x = √(6*6)

∴ x = 6 Ans.

also read similar questions: Which equations have the same value of x as 2/3(6x+12)=-24? Check all that apply.1. 4x+8=24 2. 9x+18=-24 3. 4x+12=-24 4. 18x+36/2=-24 5. 4x=-36 6. 4x=-32 7. x=-... brainly.com/question/6702722?referrer

8 0

2 years ago